A Nice Algebra Problem | Math Olympiad | X=?

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How to solve for X=? in this algebra equation
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[@streptococcuspneumoniae-ix1ve]

x = 4-x
2x = 4
x =2

[@darioc1967]

Good

[@cachotrelles4715]

👌👌👏👏

[@natanakapchits6849]

How to use root with "i"? How to check is that roots are work for that problem?

[@MathSync]

i ❤ Mathematics

[@joseeoliviero6078]

You lost the 4rth root? You should have 4 solutions but you missed an opportunity to do another perfect square:
(X^2 - (x-4)^2)
You squared the right side but could have treated this a perfect square instead. Do you agree?

[@massimoarmillotta2705]

No. That equation has degree = 3, not 4. The degree of an equation is the maximum power of x when the equation is reduced at its minimum form. If you try, you'll see that x^4 will disappear

[@joseeoliviero6078]

I understand now. Thanks

[@ryandeboer175]

Just the idea that the half of 4 will give the ±x is enough to solve this

[@user-nr4uh5zr7i]

Тут так сложно решать не надо. Вариант решения, это использовать свойство отрицательных чисел умножаемых на самого себя становиться положительным числом. Не сложно увидеть, что в данном примере Х=2, так как 2-4=-2. А -2 в четвёртой степени это 16.
There is no need to make such a difficult decision here. A solution is to use the property of negative numbers multiplied by themselves to become a positive number. It is not difficult to see that in this example X = 2, since 2-4 = -2. A -2 to the fourth power is 16.

[@darioc1967]

Help (x+y)^x^1/2=(x-y)^y^1/2

[@user-hz5ne2rl5e]

In x^4=(x-4)^4 both sides of the equation are positive for all x. Taking the 4th root of both sides and consider all possibilities for LHS and RHS: ++, +-, -+, --. The solution is -x=x-4 or x=-(x-4) => x=2 is a real root. If you are looking for complex conjugates, then the factor theorem and (x-2)(x^2-4x+8)=0.

[@Halimamessaoudi-vl3dp]

yes this correct

[@mohamedsalah5525]

16

[@JohnMayer-ql5fd]

Can we take the fourth root in the first step?

[@Iloveminecraftverymuch]

Why not?😊

[@JohnMayer-ql5fd]

@@Iloveminecraftverymuch Why?

[@cosmolbfu67]

yes but we'll get one solution
x^4=(x-4)^4
take 4th root
x=|x-4|
x=x-4, x=-x+4
So x=2

[@massimoarmillotta2705]

No. This equation has degree = 3, not 4 as I told before. The degree is the maximum power of X when the equation is reduced at its minimum form. If you make calculations, you'll see that x^4 will disappear

[@Jeffsobrinho]

Professor, as the X has power of 4, shouldn't the equation have 4 solutions?

[@massimoarmillotta2705]

No. This is a 3rd degree equation. The degree of an equation is the maximum power of X when the equation is reduced at its minimum form and that one is not the minimum form.

[@user-hz5ne2rl5e]

@@massimoarmillotta2705 He's right. There are 4 roots to the equation in the power of 4. x=2 are two repeated roots. x=2-i and x=2+i are two complex conjugates.

[@massimoarmillotta2705]

This is not a power of 4 equation but 3. So there are only 3 solutions

[@snarkybuttcrack]

@@user-hz5ne2rl5e x=2 is not a repeated root

[@user-hz5ne2rl5e]

@@snarkybuttcrack You are correct. It's not a repeated root. I made a mistake, not checking it if it is.

[@zougaghabdelmajid5449]

X#0 chercher les racines 4eme de l unité 1;-1;i et -i du in l appelle a une telle racine
Résoudre ax = x-4 du premier degré....

[@dardoburgos3179]

X= 2.

[@user-kp1rd1dh4s]

Надо сначала вычислить дискриминант, а потом делать вывод о решении квадратного уравнения. Все хорошо, но не рационально решено банальное квадратное уравнение. Зачеркивание в алгебре допускается при уничтожении слагаемых с разными знаками, а вот при сокращении дроби необходимо писать результат, даже если это 1.

[@natanakapchits6849]

Первый раз такое слышу. Какой смысл писать единицу при сокращении, если в произведении она роли не играет?

[@user-kp1rd1dh4s]

@@natanakapchits6849 математика- точная наука и сокращение дроби-это деление числителя и знаменателя на одно и то же число, при делении должно получится частное. Сейчас сплошь и рядом этим пренебрегают, даже репетиторы, с моей точки зрения эта мелочь однажды может по невнимательности привести к ошибке.

[@12wurst34]

Not 4 me!

[@alexeyevgenevich9821]

Х = 2, поясню почему:
2^4 = (2-4)^4. Обе части получились 16

[@rabotaakk-nw9nm]

А где два мнимых корня? 😮

[@alexeyevgenevich9821]

@@rabotaakk-nw9nm кстати, мнимые корни в школьную программу по математике не входили, по крайней мере, когда я учился

[@rabotaakk-nw9nm]

​@@alexeyevgenevich9821Кстати, это - Ваша проблема.

[@natanakapchits6849]

​@@alexeyevgenevich9821 как же проверить эти корни с мнимыми единицами? Нам просто говорили, что квадратные корни из отрицательных чисел не вычисляется и следовательно мы такие корни не принимали к решению уравнения.

[@sayyestoamerican]

Dude what kind of mushrooms you’re using square root of -16, seriously?
Answer is 2

[@errorxd3423]

I don't like maths🤢......🤮

[@user-yg2qr8ph2j]

becouse you are stupid